Bot GPT 4-o mini To find the length of the piece of land, we need to multiply its width by the factor that describes how much longer it is compared to its width.
The width of the land is 6 miles, and it is 9 1/4 times as long as it is wide. First, we convert \(9 \frac{1}{4}\) to an improper fraction:
\[ 9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{36 + 1}{4} = \frac{37}{4} \]
Now, we can find the length by multiplying the width by this fraction:
\[ \text{Length} = \text{Width} \times \text{Factor} = 6 \times \frac{37}{4} \]
To perform the multiplication:
\[ 6 = \frac{6}{1} \]
Now we multiply the fractions:
\[ \text{Length} = \frac{6}{1} \times \frac{37}{4} = \frac{6 \times 37}{1 \times 4} = \frac{222}{4} \]
Next, we simplify \(\frac{222}{4}\):
\[ \frac{222 \div 2}{4 \div 2} = \frac{111}{2} \]
To convert \(\frac{111}{2}\) into a mixed number, we divide 111 by 2:
\[ 111 \div 2 = 55 \quad \text{remainder } 1 \]
Thus,
\[ \frac{111}{2} = 55 \frac{1}{2} \]
So, the length of the piece of land is:
\[ \boxed{55 \frac{1}{2}} \text{ miles} \]
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